Equations with fractions

Solve (x + 3)/2 = (x + 18)/4

The aim is to get x on its own. Whatever we do to one side, we do to the other, so the equation stays balanced. This one takes 4 steps.

(x + 3)/2 = (x + 18)/4The question.
Step 1: Multiply by 4 on both sides ×4

There are fractions. Multiply both sides by 4 to clear them: 4 is the smallest number that all the bottoms go into.
2(x + 3) = x + 18
Multiplying every term by the same number keeps the balance.
Step 2: Expand the brackets on both sides expand

Expand the brackets first, so you can see all the x terms.
2x + 6 = x + 18
Multiply the number outside by everything inside.
Step 3: Subtract x on both sides −x

There’s x on both sides. Take away x on both sides so x is only on one side. Choosing the smaller x keeps the numbers positive.
x + 6 = 18
On the right, the x cancels out. Now there’s no x on the right.

You can add or take away x terms, just like numbers.
Step 4: Subtract 6 on both sides −6

On the left, the x part has + 6 with it. Take 6 away from both sides to get rid of it.
x = 12
On the left, the 6 cancels out. x is on its own. x = 12.

+ 6 is undone by − 6.

Answer: x = 12

Put x = 12 back into the question. If both sides come to the same number, the answer is right.

Left side: (x + 3)/2 → 15/2

Right side: (x + 18)/4 → 15/2

✓ Both sides are 15/2, so x = 12 is right.

Solve this one in Algebra Balance. You choose each step, and it explains what happened, with hints if you get stuck.